Claim against the parking area owner would not prosper as it was not the one who caused damages to your car but an unknown party. Better claim against your insurance - if you have one.
Halos lahat ng parking lot business ngayon (kahit paid parking) usually ang policy na is that they are not liable to any damages or theft in/on your car. Parang "park-at-your-own-risk" or "pasalamat-ka-meron-ka-pang-naparkingan-dito" policy.
Saka kung iisipin mo rin, pag pumasok ka sa parking lot nila, they don't inspect your car if you came in with a damaged or scratched door already. Kaya kung ikaw rin mismo yung may-ari nung parking lot, malay mo ba kung dati ng merong scratch at dents yung pinto niya at gusto ka lang kwartahan. Diba 'pre.
So malamang insurance na lang pag-asa mo pards. Good luck! Ma-karma sana yung mga ungas na yun na dumale sa tsikot mo.